Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: What is the maximum possible area of triangle? [#permalink]

Show Tags

22 May 2012, 00:17

Smita04 wrote:

What is the maximum possible area of triangle?

(1) Two sides of the triangle are 7 cm and 14 cm. (2) The triangle is inscribed in a circle and one of its sides is 7 cm.

My answer would be E.

1. Two sides are 7 and 14 but we don't know which is base and which is height. Third side is 7< x < 21. 2. We are only given one side and no info whether this is B or H.

Re: What is the maximum possible area of triangle? [#permalink]

Show Tags

22 May 2012, 07:18

I think answer is A.

Two sides are 7 an 14 so by the triangle sides property third side can be in between of 7 and 21. We need to maximise the area of triangle which is possible with these two sides and another sides so we will choose the third side as 20 (Assumption is sides are integer). Triangle with sides 7 ,14 and 20 will have the max area and this can be calculate using the below formula.

Re: What is the maximum possible area of triangle? [#permalink]

Show Tags

22 May 2012, 21:59

To maximize the area of a triangle and if you know the length of two sides make them perpendicular to maximize the area. Hence A is sufficient. However, I do have my doubts about this answer as well.. where are the experts?

Re: What is the maximum possible area of triangle? [#permalink]

Show Tags

22 May 2012, 22:19

Smita04 wrote:

Bunuel, can you please comment on this? Is it not a GMAT type question? If that is the case, then there is no point discussing it.

Hi Smita04,

This is very much a GMAT query.

Evaluating statement 1 only: Here, we know that the length of the two sides are 7 cms and 14 cms respectively. Now just picture this. Let us try to a triangle with base = 14 cm and then try to put the 7 cm side such that ther area is the maximum.

Let the side AB = 7 cm and BC = 14 cm. The figure shows 3 possibilities for AB that would result in the maximum possible area for triangle ABC. Now, we k now that area = 1/2 * base * altitude = 1/2 * BC * altitude. Now, the area will be maximum for the maximum value of the altitude. This is only possible with AB as the altitude, as in the other two cases the length of the altutide goes down. Hence, ABC is right angled and the maximum area = 1/2 * 14 * 7 We can eliminate options B, C and E.

Evaluating statement 2 only: Let us picture this.

Let side AB = 7 cm. Now depending on the size of the circle, the area of the triangle can keep increasing. Hence, statement 2 alone is insufficient. Hence D is eliminated. Answer is A.

Re: What is the maximum possible area of triangle? [#permalink]

Show Tags

06 Jun 2012, 13:36

what is OA smita? i got E as i thought it is not possible to find are untill we know which side is given what? can someone explain what is regarding maximising sides?

Re: What is the maximum possible area of triangle? [#permalink]

Show Tags

10 Oct 2012, 03:08

Smita04 wrote:

What is the maximum possible area of triangle?

(1) Two sides of the triangle are 7 cm and 14 cm. (2) The triangle is inscribed in a circle and one of its sides is 7 cm.

Good question. I feel this can be perfect GMAT question.

Q ->What is the maximum possible area of triangle ? 1) Let the third side is x which ranges from 7<x<21 where x can take any value within this range.

Now the three sides of the triangle are 7, 14, 7<x<21. Using these 3 sides numerous triangles can be made but only 1 triangle will have the maximum area , which we can find out (but it is not required to find the max area) Sufficient

2) Outright insufficient

Answer A
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Re: What is the maximum possible area of triangle? [#permalink]

Show Tags

10 Oct 2012, 09:28

1

This post received KUDOS

fameatop wrote:

Smita04 wrote:

What is the maximum possible area of triangle?

(1) Two sides of the triangle are 7 cm and 14 cm. (2) The triangle is inscribed in a circle and one of its sides is 7 cm.

Good question. I feel this can be perfect GMAT question.

Q ->What is the maximum possible area of triangle ? 1) Let the third side is x which ranges from 7<x<21 where x can take any value within this range.

Now the three sides of the triangle are 7, 14, 7<x<21. Using these 3 sides numerous triangles can be made but only 1 triangle will have the maximum area , which we can find out (but it is not required to find the max area) Sufficient

2) Outright insufficient

Answer A

(1) You are absolutely right. Since only two sides of the triangle are given, the area varies depending on the third side. Since we can make the area as small as we wish and the third side must be between 7 and 21, the area must be finite for every one of these possible triangles. So, there must be a maximum, and because this is a DS question, we are not supposed to find that maximum. Trigonometry is out of question on the GMAT, but even without it, we can figure out when the area is maximum.

Since the area of a triangle is the same regardless which side we take as a base, we can consider 14 (denoted by BC in the attached drawing) as a constant base, and look at the various triangles that can be formed. Angle ABC varies between 0 and 180, with the side AC of constant length 7. Maximum height corresponding to BC is obtained when AB is perpendicular to BC, and in fact we now know that the maximum area will be 14*7/2 = 49. Indeed (1) is sufficient.

(2) Any triangle can be inscribed in a circle and through two given points (apart at a distance of 7) there are infinitely many circles passing through. Obviously not sufficient.

Hence answer A.

Attachments

TriangleMaxArea.jpg [ 9.9 KiB | Viewed 10491 times ]

_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: What is the maximum possible area of triangle? [#permalink]

Show Tags

09 May 2014, 02:07

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: What is the maximum possible area of triangle? [#permalink]

Show Tags

28 Sep 2015, 09:24

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: What is the maximum possible area of triangle? [#permalink]

Show Tags

31 May 2016, 23:02

EvaJager wrote:

fameatop wrote:

Smita04 wrote:

What is the maximum possible area of triangle?

(1) Two sides of the triangle are 7 cm and 14 cm. (2) The triangle is inscribed in a circle and one of its sides is 7 cm.

Good question. I feel this can be perfect GMAT question.

Q ->What is the maximum possible area of triangle ? 1) Let the third side is x which ranges from 7<x<21 where x can take any value within this range.

Now the three sides of the triangle are 7, 14, 7<x<21. Using these 3 sides numerous triangles can be made but only 1 triangle will have the maximum area , which we can find out (but it is not required to find the max area) Sufficient

2) Outright insufficient

Answer A

(1) You are absolutely right. Since only two sides of the triangle are given, the area varies depending on the third side. Since we can make the area as small as we wish and the third side must be between 7 and 21, the area must be finite for every one of these possible triangles. So, there must be a maximum, and because this is a DS question, we are not supposed to find that maximum. Trigonometry is out of question on the GMAT, but even without it, we can figure out when the area is maximum.

Since the area of a triangle is the same regardless which side we take as a base, we can consider 14 (denoted by BC in the attached drawing) as a constant base, and look at the various triangles that can be formed. Angle ABC varies between 0 and 180, with the side AC of constant length 7. Maximum height corresponding to BC is obtained when AB is perpendicular to BC, and in fact we now know that the maximum area will be 14*7/2 = 49. Indeed (1) is sufficient.

(2) Any triangle can be inscribed in a circle and through two given points (apart at a distance of 7) there are infinitely many circles passing through. Obviously not sufficient.

Hence answer A.

Statement 2 > Among all triangles inscribed in a given circle, the equilateral one has the largest area.

So if we consider side as 7, we can get the maximum area. Note that, question is asking for maximum area, not exact area. I think OA should Be D.

@bunnel: Pl help.

gmatclubot

Re: What is the maximum possible area of triangle?
[#permalink]
31 May 2016, 23:02

After days of waiting, sharing the tension with other applicants in forums, coming up with different theories about invites patterns, and, overall, refreshing my inbox every five minutes to...

I was totally freaking out. Apparently, most of the HBS invites were already sent and I didn’t get one. However, there are still some to come out on...

There is without a doubt a stereotype for recent MBA grads – folks who are ambitious, smart, hard-working, but oftentimes lack experience or domain knowledge. Looking around and at...